Gradient Method with Retards and Generalizations
SIAM Journal on Numerical Analysis
Multiparameter Iterative Schemes for the Solution of Systems of Linear and Nonlinear Equations
SIAM Journal on Scientific Computing
Relaxed Steepest Descent and Cauchy-Barzilai-Borwein Method
Computational Optimization and Applications
Acceleration schemes with application to the EM algorithm
Computational Statistics & Data Analysis
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In this paper, we propose a new method which could be considered as a modification of the Δk-method introduced for solving nonlinear fixed point problems. At each iteration of the new scheme, we evaluate the Δk steplength once and we use it twice. Various numerical results illustrate the efficiency of the new scheme. They concern the solution of a reaction-diffusion problem which exhibits a bifurcation. An additional example, involving a mixture of Poisson distributions, will be given and suggest that the new scheme could be adapted with success for an important statistical problem called the expectation-maximization problem.